10 Strategy Development & Implementation SWOT analysis Critical success factors Staffing Integration of OM w/other activities
11 Strategic Fit Organization Environment Strengths Weaknesses Opportunities Threats
12 Productivity Mathematical & intuitive definitions Number of inputs Usefulness Factors affecting
13 Compute the multifactor productivity measure for each of the weeks shown. What do the productivity figures suggest? Assume 40-hour weeks and an hourly wage of $12. Overhead is 1.5 times weekly labor cost. Material is $6 per pound. WeekOutput (units)WorkersMaterial (lbs) 130,0006450 233,6007470 332,2007460 435,4008480
16 Time Horizons Short, medium, long-range horizons Differences in horizons –Plan the system –Plan the use of the system 3 yearsNow Location, new products Production & sales planning Scheduling Our focus 3 months
22 Notes on Notation F = Forecast A = Actual (known demand) t+1 = next period, t = current period A bar over something means average e.g. = repeated addition (summation) X
23 Time Series Techniques Naïve Method –Note discrepancy from text Moving Average Exponential Smoothing
24 More Time Series Equations Exponential Smoothing (alternate version) Linear Trend
25 Depends, Inc. sells adult diapers. Monthly sales for a seven month period were as follows. MonthSales (000 units) Feb19 Mar18 Apr15 May20 Jun18 Jul22 Aug20 Plot the data Forecast sales for September using linear trend; 5 month moving average; exponential smoothing with alpha=0.2 assuming a July forecast of 19; naïve approach; weighted average of.60 for Aug,.30 for July, and.10 for June.
Seasonal Data Deseasonalizing alternatives A tourist center is open on weekends. The manager hopes to improve scheduling of part-time employees by developing a forecasting model. He assigns you this task but will ultimately take credit for your model. 26 123456 Friday149154152150159163 Saturday250255260268273276 Sunday166162171173176183
27 Associative Forecasting dependsOne items value depends on another items value Linear regression
28 The following data were collected during a study of consumer buying patterns. ObservationXYObservationXY 11574 81878 22580 91470 34084101572 43281112285 55196122488 64795133390 73083 Plot the data. Obtain a regression line. How much variance is explained? Predict Y when X=41.
30 Accuracy & Control MAD = Mean Absolute Deviation Tracking Signal = MSE = Mean squared error
31 Doug Moodie is the president of Garden Products Limited. Over the last 5 years, he has asked his vice president of marketing and his vice president of operations to provide sales forecasts. The actual sales and the forecasts are given here. Which vice president is better at forecasting? YearSalesVP MktVP Ops 1167,325170,000160,000 2175,362170,000165,000 3172,536180,000170,000 4156,732180,000175,000 5176,325165,000
33 Product Life Cycle IntroductionGrowthMaturityDecline Volume time Production method, run length & capacity Product design Process reliability
34 Dis-integrated design processes Standardization & modular design Manufacturability & value engineering Green manufacturing R&D versus benchmarking # Ideas Proposed Produced Mkt. Test Prototype Product Development
35 Computer Aided Design Used for –drafting –simulation – testing Integration w/CAM
37 Service Blueprinting Physical Evidence Customer Onstage Service Backstage Service Support Line of Interaction Line of Visibility
38 A structured and disciplined process that provides a means to identify and carry the voice of the customer through each stage of product or service development and implementation QFD is: Communication Documentation Analysis Prioritization breakthroughs Quality Function Deployment
39 Japanese QFD Results Design time reduced by ¼ to ½ Problems with initial quality decreased Comparison and analysis of competitive products became possible Communication between divisions improved
40 oldsystem newsystem productdefinition designredesign Product Design Time Line
41 Quality Function Deployment (in 75 minutes or less) Smylie Cellphone is a one-product company founded in 2004. Its product is a cell phone. The companys annual sales last year were $18 million all in the United States. The company is located in Edmond in its own 400 square foot manufacturing plant and has 4 employees. The company recently completed a five-year business plan with a goal of expanding from a one-product to a multi-product line. The plan is to expand sales by attracting new customers and penetrating foreign markets. The company wants to develop a new cell phone that will appeal to adults in both the United States and foreign markets. Smylie Cellphone has selected your team to provide quality function deployment consulting services to help develop the new product. Your team has agreed as a first phase to develop chart A-1 detailing the following: 1.Voice of the customer 2. Degree of importance 3. Company now and competitive comparison 4. Company plan 5. Improvement ratio 6. Sales point 7. Importance weight 8. Relative weight 9. Graphical competitive comparison 10. Quality characteristics 11. Relationships 12. Importance weight 13. Relative weight 14. Technical comparison 15. Special requirements 16. Correlation matrix The study must be painstaking in detail, unerring in accuracy, and completed in one hour. To show its commitment the company has agreed to have a representative available throughout the period for clarification and consultation. 1 10 1123456789 12 13 14 15 16
42 1. Voice of the customer - Identify all customer groups and collect accurate information about their wants and needs (restrict yourself to 10 needs given our time constraint) 2. Degree of importance - Identify the relative priority of each customer requirement using customer input to determine the values wherever possible. Use a scale of one to ten with ten indicating very important items. 3. Company now and competitive comparison - Rate your current product (use the worst looking wallet in your group - in the event of a dispute as to whose wallet looks the worst, the company representatives decision is final) and two competitors products on a scale of one to five with five being the best. 4. Company plan - Determine what level you plan to achieve for each customer requirement. Since WWWs resources are finite, make your improvement decisions based on steps 2 and 3. That is, choose the most important items where you can gain a clear advantage over your competitors. Use a scale of one to five with five being best. 5. Improvement ratio - Quantify the improvement planned for each customer requirement by dividing the value of the planned level by the current company rating. 6. Sales point - Identify major and minor points (front-of-the-brochure claims) by using information in columns 2 and 4. Restrict yourself to only a few sales points (perhaps two major and a minor point since we have only ten customer demands). Indicate the major points with this symbol and the minor points with this symbol. The major points are worth 1.5 and minor points are worth 1.2. 7. Importance weight - Quantify the importance of each customer requirement to your company with the following equation: Importance weight = (column 2) x (column 5) x (column 6). 8. Relative weight - Find the relative importance of each item in column 7 by summing column 7 and dividing each entry by the total. Express this as a percentage. 9. Graphical competitive comparison - Plot the information in column 3 using a different symbol for the company and two competitors. This provides a comparison at a glance between the competitors rather than forcing the analyst to hunt for information in the matrix. 10. Quality characteristics - Develop this list internally by looking at features of your current product, e.g., the stitching, type of leather, etc. 11. Relationships - Identify all relationships that quality characteristics (column 10) have on voice of the customer items (column 1). Evaluate each pair by asking if the quality characteristic in any way affects the customer demanded quality item. Indicate the strengths of relationships by using the symbols,, and for strong (9), moderate (3), and weak (1) relationships respectively. Do not expect to find relationships between every pair of requirements. 12. Importance weight - Quantify the importance of each technical requirement by multiplying the value of any relationships shown in the column of the technical requirement times the relative weight of the customer requirement. 13. Relative weight - Similar to column 8 except you total the importance weights from row 12 and divide the weight of each item by the total. Express this as a percentage. 14. Technical comparison - Identify how well you and your competitors fulfill each of the technical requirements using the same symbols and scale as in column 9. 15. Special requirements - Identify any components governed by external sources, such as FDA, UL, etc. rules. 16. Correlation matrix - Compare quality characteristics against each other to identify complementary or conflicting relationships early in the design process. Use the symbols and for strong and some positive correlation and x and for some and strong negative correlation respectively.
45 Reliability Probability Failure Normal operating conditions (remember Taguchi) Redundancy
46 Failure Rates Product failure rate (FR) expressed in terms of time FR(N) or fraction of items tested FR(%)
47 Physio-Control burns-in their defibrillators for 24 hours after they are assembled. Over the past week they have produced 300 LifePak 12s. One unit failed on the first charge discharge cycle. Compute the failure rates and mean time between failures.
48 Two items that both must work for the system to perform are said to be in series Reliability Calculations = 0.95 0.90
49 Backups (Redundancy) These two components form a parallel subsystem that improves reliability 0.80 0.70 0.95 =
50 One of the industrial robots designed by a leading producer of servomechanisms has four major components. Components reliabilities are.98,.95,.94, and.90. All components must function in order for the robot to operate effectively. What is the robots reliability? If one backup can be added, where should it be? If one 0.92 backup can be added, where should it be?
51 MTBF/TF & the Bathtub Product failure is described as f(t)=λe -λt and when the slope of this cumulative failure curve is plotted, we get a bathtub shaped curve. Time Failure Rate
52 Mean Time Between Failure Calculations P(no failure before T) = e -(T/MTBF) where: e is 2.71825 (and a calculator button) T is a specified length of time MTBF is the mean time between failures as determined by historical data Probabilities working the way they do, whats the probability of failure before T?
53 FOX intends to launch a satellite that will enhance reception of television programs everywhere and complete Rupert Murdochs plan for world domination. According to FOX engineers, the satellite will have a useful life of eight years (four times as long as a typical sitcom). Determine the probability that the satellite will: a. Last more than nine years b. Last less than twelve years c. Fail between years nine and twelve
54 Availability Complete picture of reliability
57 A work center operates 2 shifts per day 5 days per week (8 hours per shift) and has 4 machines of equal capability. This is the effective capacity. If the work center has a system efficiency of 95%, what is the expected output in hours per week?
58 Adjusting Capacity Long Term Short Term OVERUNDER
59 Break-Even Analysis $ VOLUME (x) 0 0 TC = Total Cost F = Fixed Cost V = Variable Cost assumptions?? P = Selling Price TR = Revenue
60 You are considering opening a copy service in the University Center. You estimate your fixed cost at $15,000 and the variable cost of each copy sold at $0.01. You plan to sell at $0.05. a)What is the break-even point in dollars? b)What is the break-even point in units?
62 Decision Making Alternatives States of nature Likelihood Payoffs Criterion
63 Decision Making Under Certainty The most unexciting of the decision environments... Next years demand AlternativeLowHigh Do nothing$50*$60 Expand 20 70 Subcontract 40 80 *profit in thousands
64 Decision Making Under Risk Likelihoods of the states of nature can be assigned a probability of occurrence and the payoff for each outcome can be estimated. Expected Monetary Value (EMV) Criterion
65 Clay Whybark, a soft drink vendor at Hard Rock Cafés annual Rockfest, created a table of conditional values for the various stocking sizes and crowd sizes. With the probabilities of the crowd sizes as indicated, whats the best stock size for Clay to get rich? Crowd Size AlternativeBigAverageSmall Large Stock$22 * 12 -2 Average Stock 14 10 6 Small Stock 9 8 4 Probability.30.50.20 *additional profit in thousands
66 Decision Tree Analysis 1 1 3 2 a b c $22 $12 -$2 $14 $10 $6 9 $8 $4 Squares represent decision points Circles show states of nature These lines represent alternatives
67 An entrepreneur must decide on the size of a latte stand to construct. The manager has narrowed the choice down to two: large or small. If he builds large and experiences low demand he could grin and bear it ($200), lower prices ($225), or hire street performers to attract attention ($175). If he builds small and experiences high demand he could do nothing ($175), stay open longer hours ($225), improve processes ($250), or raise prices ($200). Building large for large demand has an expected payoff of $250 and building small for small demand has an expected payoff of $175. There is a 0.7 probability of high demand and 0.3 probability of low demand. What size stand should be constructed to slake the unquenchable thirst of caffeine addicts?
68 DMUR Expected payoff under certainty Expected value of perfect information EVPI = EPUC - EMV
69 Four alternative manufacturing methods are being considered for a new product. Profitability, which depends on method of manufacture and level of consumer acceptance, is anticipated as shown here: Profit ($ Thousands from Product) Projected Acceptance MethodLowMedHighVery High 1100200300 600 2175300400 500 3250300350 425 4100300400 450 Probability0.250.350.20 0.20 Which method is best? Whats the most the company should invest in analyzing the situation?
70 Decision Making Under Uncertainty Characterized by a complete lack of knowledge regarding the likelihood of occurrence for each state of nature –Maximax –Maximin –Minimax regret –Laplace/equally likely
71 Given the following conditional value table, determine the appropriate decision under uncertainty using: Maximax Maximin Minimax Laplace Very FavorableAverageUnfavorable Build new plant$350,000$240,000-$300,000 Subcontract$90,000$180,000-$20,000 Overtime$110,000-$10,000$60,000 Do nothing$0
72 A firm produces a perishable food product at a cost of $10/case and sells it for $15. The firm considers possible demands of 100, 200, and 300 cases. If demand is less than production, the excess is discarded but if demand is more than production the firm will produce the shortfall at $18/case. If P(100)=.2, P(200)=.2 and P(300)=.6, how much should be produced?
73 A decision maker faced with four alternatives and four states of nature develops this payoff table. If the decision maker knows nothing about the chances of occurrence of each state of nature, what would reasonable decisions be? How do your conclusions change if these values represent costs instead of revenues? s1s2s3s4 d1149105 d2111087 d3910 11 d48101113
74 Process Selection & Facility Layout Chapter 6
75 Determinants Degree of customization –Make-to-order –Assemble-to-order –Make-to-stock Volume
79 Group Technology Part families Setup time, transportation, congestion Service applications
80 Layout Considerations Material handling Information flows Environment/aesthetics Capacity Costs
81 Assembly-line Balancing Cycle Time (CT) Operating Time Output Output = Minimum # Stations = Task Times Cycle Time
82 Line Balancing Rules Obey precedence requirements Obey scheduling rule(s) Fill up as much time as possible at each station Compute efficiency & balance delay (idle time) since youll probably have to defend your balance
83 Use this table to balance the line for an output of 320 units in an 8 hour work day. Create a precedence diagram and balance the line using the largest- process-time rule and the smallest-process-time rule. Work times are in seconds. TaskTimePred Z30-- Y42-- X12Z, Y W6Z V48X U24W T W S36T, V R30U, S
84 The Mach 10 is a one-person sailboat designed to be used in the ocean. 200 minutes are available each day to manufacture the Mach 10. The daily demand is 60 boats. Task(minutes)Follows a1- b1a c2a d1c e3c f1c g1d, e, f h2b I1g, h a)Draw the precedence diagram. b)Determine the percentage of idle time.
85 An assembly line with 30 activities is to be balanced. The total amount of time to complete all 30 activities is 42 minutes. The longest activity takes 2.4 minutes and the shortest takes 0.3 minutes. The line will operate for 450 minutes per day. What are the maximum and minimum cycle times? What output rate will be achieved by each of those cycle times? Suppose this line is balanced using ten workstations and a finished product can be produced every 4.2 minutes. What is the production rate in units/day? What is the assembly line efficiency?
87 Registration at UCO has always been a time of emotion, commotion, and lines as students move among four stations as shown here. 450 students moved from paperwork station A to advising B, and 550 went directly from A to picking up class cards C. Graduate students proceeded from A to the Bursar D. Adjacent stations are 30 apart. a)What is the load x distance of the layout shown? b)Provide an improved layout and compute its cost. ABCD A--45055050 B350--2000 C00--750 D000-- ABC D
88 Use the information in the grid to assign departments to a 3x3 office space. Department 1 2 3 4 5 6 7 8 X X X O O O O A A A A A A A A A A A E E E E
90 Linear Programming Used when scarce resources are used by competing products. Objective Decision variables Constraints Parameters
91 I make two different kinds of moonshine to supplement my meager wages. Rotgut sells for $8 per jug and White Lightning, the premium brand, sells for $12/jug. Below is a list of ingredients for a batch of each type: RotgutWhite Lightning Corn12 Sugar32 Jugs22 Hours23 I have on hand the following:40 bushels corn, 70 pounds sugar, 50 jugs, and 72 hours (before the revenoors come to bust up my still) How much of each flavor should I make?
93 Model formulation Identify decision variables Write an objective function Identify all constraints Write constraints with all decision variables on the left side of an inequality Solve it graphically, using Excel, or simplex
94 Graphical Solutions Work with only two decision variables Sketch axes Plot each constraint (pick (0,y) and (x,0)) Identify feasible region Find vertices of feasible region Evaluate objective function
95 Solve the following problem graphically: Maximize Z = 4X + 6Y Subject toX + 2Y 8 5X + 4Y 20 X,Y 0
96 The grand Valley Company, run by the J Motwani family, produces two products, bed mattresses and box springs. A prior contract requires that the firm produce at least 30 mattresses or box springs, in any combination per week. In addition, labor union agreements demand that stitching machines be kept running at least 40 hours per week, which is one production period. Each box spring takes 2 hours of stitching time, while each mattress takes one hour on a machine. Each mattress produced costs $20; each box spring costs $24. a)Write the objective function and constraints in canonical form. b)Solve graphically.
97 Linear Programming in Excel One of Excels useful features is the ability to solve linear programming problems (especially those beyond our graphical abilities). The feature is invoked by creating a spreadsheet containing the objective function and constraints, selecting Tools from the main menu, and Solver from the submenu
98 Here is an Excel version of the moonshine problem The top view shows formulas and the bottom view shows initial calculations. BCDEFG 3 1624 4 RotgutWhite Lightning 5 22=D5*D3+C5*C3Profit 6 7Corn12=D7*$D$5+C7*$C$5<=40 8Sugar32=D8*$D$5+C8*$C$5<=70 9Jugs22=D9*$D$5+C9*$C$5<=50 10Hours23 =D10*$D$5+C10*$C $5<=72 BCDEFG 3 $16.00$24.00 4 RotgutWhite Lightning 5 22 $ 80.00Profit 6 7Corn126<=40 8Sugar3210<=70 9Jugs228<=50 10Hours2310<=72
99 Once the basic set of equations has been entered, launch Solver and fill in the dialog boxes with references to your sheet. Target cell - The objective function value (E52) Equal to - Choose max or min based on the problem By changing cells - The decision variables (C52:D52) Subject to the constraints - Add all constraints one at a time by referencing their function values (e.g., the amount of corn used, E47 must be less than the amount of corn on hand, G47) Once all constraints have been entered, choose Options and check the boxes for Assume Linear Model and Assume Non-Negative. Finally, choose Solve and wait for Excel to work its magic
100 Solver Output Reports Answer Report - contains the basic answer to the problem and reveals which constraints had an impact on your situation. Sensitivity Report - tells you reduced costs and shadow prices Limits Report - dont bother asking for this one. We wont use its information.
101 The value of the objective function at the optimal solution The optimal values of the decision variables If a constraint is not binding, then we have some left over (slack) when we implement the optimal solution. We have 10 pounds of sugar and 7 hours to spare. A binding constraint is one that limits the value our objective function can assume. We use up all of our corn and jugs (we have no slack). Microsoft Excel 11.0 Answer Report Worksheet: [Moonshine.xls]Formulation Report Created: 10/2/2006 1:09:33 PM Target Cell (Max) CellNameOriginal ValueFinal Value $E$5 $ 520.00 Adjustable Cells CellNameOriginal ValueFinal Value $C$5Rotgut10 $D$5White Lightning15 Constraints CellNameCell ValueFormulaStatusSlack $E$10Hours65$E$10<=$G$10Not Binding7 $E$7Corn40$E$7<=$G$7Binding0 $E$8Sugar60$E$8<=$G$8Not Binding10 $E$9Jugs50$E$9<=$G$9Binding0
102 A one unit in(de)crease in the original amount of corn available will in(de)crease our profit by this amount Increases or decreases within these ranges will result in the same product mix (but a different objective function value). Extra amount of resource needed for a binding constraint to become non-binding. Note that this doesnt apply to non- binding constraints, hence the huge amounts indicated. Amount of resource to be taken away for a non-binding constraint to become binding, or a binding constraint to become more so. Microsoft Excel 11.0 Sensitivity Report Worksheet: [Moonshine.xls]Formulation Report Created: 10/2/2006 1:09:33 PM Adjustable Cells FinalReducedObjectiveAllowable CellNameValueCostCoefficientIncreaseDecrease $C$5Rotgut1001684 $D$5White Lightning1502488 Constraints FinalShadowConstraintAllowable CellNameValuePriceR.H. SideIncreaseDecrease $E$10Hours650721E+307 $E$7Corn408 710 $E$8Sugar600701E+3010 $E$9Jugs504 510
107 Visual Workplace Big picture Performance Housekeeping
108 TECHNICAL APPROACHES Ergonomics Work Measurement –ignorance –historical data –direct time study –predetermined time study –work sampling
109 Direct Time Study Method Define tasks Determine sample size Take measurements Rate performance
110 What sample size should be used: a)if there should be a.95 probability that the value of the sample mean is within 2 minutes, given that the standard deviation is 4 minutes? b)there should be a 90% chance that the sample mean has an error of 0.10 minutes or less when the variance is estimated as 0.50 minutes?
111 Direct Time Study Observed Cycle Time (OT) = average observed time Normal Time (NT) = OT x Performance Rating –< 100% is slow –> 100% is fast Standard Time (ST) = NT/(1- Allowance Factor) –breaks –fatigue –downtime
112 Work Sampling Percentage of time on a task Define task Spy randomly
113 If a worker has times of 8.4, 8.6, 8.3, 8.5, 8.7, 8.5, a performance rating of 90%, what is the normal time? If the allowance factor is 15%, what is the standard time for this operation?
114 A part-time employee who rolls out dough balls at a pizza restaurant was observed over a 40 hour period for a work sampling study. During that time, she prepared 550 pieces of pizza dough. The analyst made 50 observations and found this employee not working four times. The overall performance rating was 1.10. The allowance for the job is 15%. Based on these data, what is the standard time for preparing pizza dough?
115 Labor Standards Labor Efficiency Variance measures the difference between expected and actual costs.
116 A trucking companys labor standard is 320 miles/8 hour shift. Drivers logged 31,525 miles and recorded 822 hours of work. If drivers are compensated $15/hour, what is the labor efficiency variance? If the standard is lowered 10% what is the labor efficiency variance?
117 A farming conglomerate expects a four person hay crew to place 1,750 bales in the barn per day. The labor cost is $600 per day for a crew of four. In the past four days 8,100 bales have been harvested. Should the conglomerate be pleased with this level of output?
127 ANALYSES (semi- breakeven)Locational cost volume (semi- breakeven) –minimizes total costs in desired output range Factor rating method –creates scores for sites based on factors & importance $ VOLUME SITE Q SITE X SITE W
128 Fixed and variable costs for four potential plant sites are below: Enumclaw$100K$30 Renton$150K$20 Kent$200K$35 Snoqualmie$250K$11 Over what range of output is each alternative superior? If the anticipated output is 8,000 units per year, which location is best? FixedVariable LocationPer YearPer Unit
130 ANALYSES Transportation Model –minimizes transportation costs using LP Center of gravity & simple median models –minimizes transportation costs using geometry
131 A chain of insurance firms in OK needs to locate a central office from which to conduct internal audits and other periodic reviews of its facilities. Each site, except for Players, will be visited three times a year by Carroll Fisher, who will drive from the central office. Players will be visited five times a year. What coordinates represent the distance-minimizing central location for this office? What other factors should be considered? CityXY Hugo9.23.5 Durant7.32.5 Players7.81.4 Blackwell5.08.4 Waurika2.86.5 Velma5.52.4 Ardmore5.03.6 Hooker3.88.5
141 Flow Chart Example: Self-Serve Gas Before Improvement Drive in check price self serve? to pump shut off engine walk to pay station yes no check card transmitapproved? turn on pump yes no back to car pump gas walk to booth wait employee totals charges check accuracy prepare receipt sign copy copy to file copy to wallet return to car on the road again
142 Flow Chart Example: Self-Serve Gas After Improvement Drive in check price self-serve? no yes go to pump shut off engine insert card in pump check credit card wait approved? no yes wait for receipt store in system copy to wallet on the road again pump gas
143 CHECK SHEETS Data collection Preliminary analysis
144 Either a Tally Sheet Contents mixed Poor taste Low temperature Utensils dirty Price issue Other
151 Scatter Diagram Exam Score Homework Problems Class 1 Class 2
152 Cause & Effect Diagrams Also known as fishbone diagrams or Ishikawa diagrams, after their creator Kaoru Ishikawa In general, used to find and cure causes (NOT symptoms) of problems
153 Basic Cause Effect Diagram Main Cause Level 1 cause Level 2 cause Level 1 cause Problem to be Resolved (effect)
154 Cause & Effect Example LATE PIZZA DELIVERY FRIDAY & SATURDAY MANPOWERMETHODS MATERIALSMACHINES Drivers lost Chef late Lack of ingredients Small ovens Large order snafus Bad cars Poor dispatching
160 Arc Node Activity Critical Path Dummy activity AOA AON PERT/CPM Format
161 BT Corp. would like to determine ES, EF, LS, LF and slack for each activity. The total project completion time and the critical path should also be determined. Activity times and predecessors are: ActPredTimeActPredTime A--6EB4 B 7FB6 CA3GC, E10 DA2HD, F7
163 Probabilistic Pert 3 Time Estimates –Optimistic –Pessimistic –Most likely Mean Standard deviation & variance Z-score
164 Probabilistic PERT Given the sequence of activities with optimistic, most likely, and pessimistic times, determine the expected completion time of the project and the variance. What is the probability the project can be completed in 24 days or less? What deadline yields a 90% probability of finishing on time? 4, 7, 106, 9, 137, 10, 13
165 The estimated times and immediate predecessors for the activities in a project at Caesar Douglass retinal scanning company are given in the table below. Assume that the activity times are independent. ActivityPredamb A--91011 B--41016 CA91011 DB58 1.Calculate the expected time and variance for each activity 2.What is the expected completion time of each path? 3.What is the variance of each path? 4.If the time to complete AC is normally distributed, what is the probability it will be finished in 22 weeks or less? 5.If the time to complete BD is normally distributed, what is the probability it will be finished in 22 weeks or less? 6.Why is the probability that the critical path will be finished in 22 weeks not necessarily the probability that the project will be finished in 22 weeks?
166 Project Crashing Crashing a project involves paying more money to complete a project more quickly. Since the critical path determines the length of a project, it makes sense to reduce the length of activities on the critical path. CP activities should be reduced until the project is reduced to the desired length or you are paying more per day than you save. If you have multiple CPs, they should be shortened simultaneously.
167 Crashing (Time/Cost Tradeoffs) Given the project specifications shown, how fast can the project be finished and how much will it cost? Act.TimeMinimum$Cost/dayPredecessor A 10 6 50 -- B 6 3 30 -- C 2 2 -- B D 4 2 40 C E 6 4 80 A F 8 5 100 D, E
168 Determine the cheapest completion time and cost for this project if it has a fixed cost of $1000 per day. ACTIVITYREQTIMEMIN TIME$/DAY 1 -- 10 5 800 2 1 20 15 650 3 2 25 15 400 4 2 20 15 700 5 3,4 15 13 900 6 5 15 101050 7 1 60 45 300 8 6,7 5 4 850